Imagine the varying frequency generator, which feeds this frequency to the oscilloscope.
Oscilloscope is turned to show signal spectra with FFT.
The image on the screen of the oscilloscope is as expected: single peak, traveling from 1 kHz to 50 kHz. Of course, my generator is not ideal, it gives a number of harmonics with less magnitude. But the strange thing happens: if my peak goes from 1 kHz to 50 kHz, the other peak appears at 50-60 kHz, and goes to lower frequencies towards mine peak. At time of appear, it's hardly noticeable, but in the end it's almost half of main frequency. Whenever varying frequency comes to it's maximum (50 kHz), ghost frequency almost approaches it. At this moment my generator drops back frequency to 1 kHz, ghost frequency disappears and process starts again.
What causes such a behaviour?
PS: I think it's more mathematical question, rather then physical or electronic.
PPS: I have some decisions, but don't want to spoil the question.